Question

Which of the following products in a hydrogen atom is independent of principal quantum number $n$ ?

• A. $v_r$
• B. $v_n$
• C. $E_r^2$
• D. $E_n$

Answer 1

The correct option is B $v_n$

The velocity of revolving electron is:
$v=\frac{e^2}{2nh{ϵ}_0}$

Hence, $v_n=\frac{e^2}{2nh{ϵ}_0}\left(n\right)$
$v_n=\frac{e^2}{2h{ϵ}_0}$

The product thus obtained does not contain principal quantum number(n) hence $v_n$ is independent of $n$.